Is it possible to store a variable of List type on an attribute of a database entity?
Short answer: No.You have to do filemaker style tricks of packing ids into a string, or create another 1:n table
As you said, the answer is No.
When you model databases, the way to use "Lists" is have 1:N Entity association, as you said.
The correct way to model databases does not suggest you to have lists in a single field. It is not an "atomic" value, violating the 1NF.